Physics and Mathematics of hydrodynamic and wave turbulence / Physique et Mathématiques de la turbulence hydrodynamique et de la turbulence d'ondes

Collection Physics and Mathematics of hydrodynamic and wave turbulence / Physique et Mathématiques de la turbulence hydrodynamique et de la turbulence d'ondes

Organizer(s) Chevillard, Laurent ; Cortet, Pierre-Philippe ; Mordant, Nicolas ; Saint-Raymond, Laure ; Shatah, Jalal

Date(s) 26/05/2025 - 30/05/2025

linked URL https://conferences.cirm-math.fr/3173.html

00:00:00 / 00:00:00

7 14

On anomalous diffusion Lecture 1

Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence. In this talk we construct a class of incompressible vector fields that have many of the properties observed in a fully turbulent velocity field, and for which the associated scalar advection-diffusion equation generically displays anomalous diffusion. We also propose an analytical framework to study anomalous diffusion, via a backward cascade of renormalized eddy viscosities. Our proof is by “fractal” homogenization, that is, we perform a cascade of homogenizations across arbitrarily many length scales.

Information about the video

Date of recording 28/05/2025
Date of publication 20/06/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20356203
Cite this video Vicol, Vlad (28/05/2025). On anomalous diffusion Lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20356203
URL https://dx.doi.org/10.24350/CIRM.V.20356203

Domain(s)

Analysis of PDEs

Bibliography

ARMSTRONG, Scott et VICOL, Vlad. Anomalous diffusion by fractal homogenization. Annals of PDE, 2025, vol. 11, no 1, p. 2. - https://doi.org/10.1007/s40818-024-00189-6
ARMSTRONG, Scott et VICOL, Vlad. Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas. arXiv preprint arXiv:2503.11744, 2025. - https://doi.org/10.48550/arXiv.2503.11744

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